Analysis of Scatter

We now return to the question of determining the uncertainty in a variable arising from scatter. Let , be different readings of the variable obtained from distinct but nominally identical (similar) experiments. The mean and variance for the set are formally defined as

and the standard deviation is equal to . The quantity in the definition of arises from the loss of one degree of freedom in forming the sum due to the presence of . If is large, the probability distribution function of the variable can be assumed to be Gaussian in view of the central limit theorem (refer Probability Density Function Approach of Lecture 3). Hence, the scatter of values about the mean follows the formula